A fuel injector is described in U.S. Pat. No. 4,759,335, which has a valve needle that has a maximum diameter at a flow-off edge, and which has a valve seat acting together with the valve needle using a valve seat, the valve seat widening, starting from the sealing seat, up to a discharge edge, and the flow-off edge of the valve needle being offset backwards, in relation to the flow direction, with respect to the discharge edge of the valve seat, when the fuel injector is closed. The fuel injector sprays the fuel at a predetermined jet angle into a combustion chamber of an internal combustion engine. The disadvantage of this arrangement is that an inadmissibly high jet angle spread may occur, at too low or too great a back offset of the flow-off edge.